清華微積分高等數(shù)學(xué)課件第六講導(dǎo)數(shù)與微分二(已修改)
2025-01-28 06:42 本頁面
【正文】 2022/2/13 1 作 業(yè) 6(3) (6) (9) (11) (14) (17). 9(4) (8) (15) (21). 10(8). 11(2). 12(2). P67 習題 2022/2/13 2 二、高階導(dǎo)數(shù) 第六講 導(dǎo)數(shù)與微分 (二 ) 一、導(dǎo)數(shù)與微分的運算法則 2022/2/13 3 一、導(dǎo)數(shù)與微分的運算法則 1. 四則運算求導(dǎo)法則 則可導(dǎo)在設(shè)函數(shù) ,)(),( xxvxu且可導(dǎo)在函數(shù) ,)()()1( xxvxu ?)()(])()([ xvxuxvxu ??????且為常數(shù)可導(dǎo)在函數(shù) ),()()2( CxxuC)(])([ xuCxuC ???2022/2/13 4 且可導(dǎo)在函數(shù) ,)]()([)3( xxvxu ?)()()()(])()([ xvxuxvxuxvxu ????????且可導(dǎo)在函數(shù) ,)()()4( xxvxu2)]([)()()()(])()([xvxvxuxvxuxvxu ???????)0)(( ?xv2022/2/13 5 )()( xvxuy ??設(shè))()()()( xxvxuxxvxxu ??? ?????vxuxxvu ??? ????? )()()()()()( xvxuxxvxu ??? ?[證 ] (3) xvxuxxvxuxy??????? ????? )()()()()()(])()([limlim00xvxuxvxuxvxuxxvxuxyyxx??????????????? ????????? 可導(dǎo)必連續(xù) )()()()( xvxuxxvxxuy ?????? ???2022/2/13 6 的導(dǎo)數(shù)求函數(shù)例2s i nlnc o s24]7[35????? xxxxyxxxx1s i n2125 24 ????[解 ] )2( s i n)( l n)( c o s2)(4)( 35 ?????????? xxxx)2s i nlnc o s24( 35 ??????? xxxxy2022/2/13 7 )c oss i n()(ta n ???xxxxxxxx2c os)(c oss i nc os)(s i n ??????.s e cc os1c os)s i n(s i nc osc os222xxxxxxx??
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